'''simple docstring'''






import torch

from diffusers import DDPMParallelScheduler

from .test_schedulers import SchedulerCommonTest







class lowercase_       (		_UpperCamelCase			):







   """simple docstring"""

   __lowerCAmelCase         =   (DDPMParallelScheduler,)
   def 	__UpperCAmelCase   (      self      :			str, **UpperCamelCase__      :			List[str]     )  ->			Tuple:
        _A    		=  {
            'num_train_timesteps': 10_00,
            'beta_start': 0.0_001,
            'beta_end': 0.02,
            'beta_schedule': 'linear',
            'variance_type': 'fixed_small',
            'clip_sample': True,
        }

        config.update(**UpperCamelCase__     )
        return config
   def 	__UpperCAmelCase   (      self      :			List[Any]     )  ->			Any:
        for timesteps in [1, 5, 1_00, 10_00]:
             self.check_over_configs(num_train_timesteps=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Optional[Any]     )  ->			Optional[int]:
        for beta_start, beta_end in zip([0.0_001, 0.001, 0.01, 0.1], [0.002, 0.02, 0.2, 2]     ):
             self.check_over_configs(beta_start=UpperCamelCase__, beta_end=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			List[Any]     )  ->			List[str]:
        for schedule in ["linear", "squaredcos_cap_v2"]:
             self.check_over_configs(beta_schedule=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Tuple     )  ->			str:
        for variance in ["fixed_small", "fixed_large", "other"]:
             self.check_over_configs(variance_type=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			List[Any]     )  ->			Union[str, Any]:
        for clip_sample in [True, False]:
             self.check_over_configs(clip_sample=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Tuple     )  ->			List[str]:
        self.check_over_configs(thresholding=UpperCamelCase__     )
        for threshold in [0.5, 1.0, 2.0]:
             for prediction_type in ["epsilon", "sample", "v_prediction"]:
                  self.check_over_configs(
                      thresholding=UpperCamelCase__, prediction_type=UpperCamelCase__, sample_max_value=UpperCamelCase__, )
   def 	__UpperCAmelCase   (      self      :			Optional[Any]     )  ->			Dict:
        for prediction_type in ["epsilon", "sample", "v_prediction"]:
             self.check_over_configs(prediction_type=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Tuple     )  ->			Tuple:
        for t in [0, 5_00, 9_99]:
             self.check_over_forward(time_step=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Tuple     )  ->			Optional[int]:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        assert torch.sum(torch.abs(scheduler._get_variance(0     ) - 0.0     )     ) < 1e-5
        assert torch.sum(torch.abs(scheduler._get_variance(4_87     ) - 0.00_979     )     ) < 1e-5
        assert torch.sum(torch.abs(scheduler._get_variance(9_99     ) - 0.02     )     ) < 1e-5
   def 	__UpperCAmelCase   (      self      :			Union[str, Any]     )  ->			Optional[Any]:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  len(UpperCamelCase__     )

        _A    		=  self.dummy_model()
        _A    		=  self.dummy_sample_deter
        _A    		=  self.dummy_sample_deter + 0.1
        _A    		=  self.dummy_sample_deter - 0.1

        _A    		=  samplea.shape[0]
        _A    		=  torch.stack([samplea, samplea, samplea], dim=0     )
        _A    		=  torch.arange(UpperCamelCase__     )[0:3, None].repeat(1, UpperCamelCase__     )

        _A    		=  model(samples.flatten(0, 1     ), timesteps.flatten(0, 1     )     )
        _A    		=  scheduler.batch_step_no_noise(UpperCamelCase__, timesteps.flatten(0, 1     ), samples.flatten(0, 1     )     )

        _A    		=  torch.sum(torch.abs(UpperCamelCase__     )     )
        _A    		=  torch.mean(torch.abs(UpperCamelCase__     )     )

        assert abs(result_sum.item() - 1_153.1_833     ) < 1e-2
        assert abs(result_mean.item() - 0.5_005     ) < 1e-3
   def 	__UpperCAmelCase   (      self      :			List[str]     )  ->			Optional[int]:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  len(UpperCamelCase__     )

        _A    		=  self.dummy_model()
        _A    		=  self.dummy_sample_deter
        _A    		=  torch.manual_seed(0     )

        for t in reversed(range(UpperCamelCase__     )     ):
             # 1. predict noise residual
             _A    		=  model(UpperCamelCase__, UpperCamelCase__     )

             # 2. predict previous mean of sample x_t-1
             _A    		=  scheduler.step(UpperCamelCase__, UpperCamelCase__, UpperCamelCase__, generator=UpperCamelCase__     ).prev_sample

             _A    		=  pred_prev_sample

        _A    		=  torch.sum(torch.abs(UpperCamelCase__     )     )
        _A    		=  torch.mean(torch.abs(UpperCamelCase__     )     )

        assert abs(result_sum.item() - 258.9_606     ) < 1e-2
        assert abs(result_mean.item() - 0.3_372     ) < 1e-3
   def 	__UpperCAmelCase   (      self      :			Dict     )  ->			Any:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config(prediction_type='v_prediction'     )
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  len(UpperCamelCase__     )

        _A    		=  self.dummy_model()
        _A    		=  self.dummy_sample_deter
        _A    		=  torch.manual_seed(0     )

        for t in reversed(range(UpperCamelCase__     )     ):
             # 1. predict noise residual
             _A    		=  model(UpperCamelCase__, UpperCamelCase__     )

             # 2. predict previous mean of sample x_t-1
             _A    		=  scheduler.step(UpperCamelCase__, UpperCamelCase__, UpperCamelCase__, generator=UpperCamelCase__     ).prev_sample

             _A    		=  pred_prev_sample

        _A    		=  torch.sum(torch.abs(UpperCamelCase__     )     )
        _A    		=  torch.mean(torch.abs(UpperCamelCase__     )     )

        assert abs(result_sum.item() - 202.0_296     ) < 1e-2
        assert abs(result_mean.item() - 0.2_631     ) < 1e-3
   def 	__UpperCAmelCase   (      self      :			Optional[int]     )  ->			Tuple:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  [1_00, 87, 50, 1, 0]

        scheduler.set_timesteps(timesteps=UpperCamelCase__     )

        _A    		=  scheduler.timesteps

        for i, timestep in enumerate(UpperCamelCase__     ):
             if i == len(UpperCamelCase__     ) - 1:
                  _A    		=  -1
             else:
                  _A    		=  timesteps[i + 1]

             _A    		=  scheduler.previous_timestep(UpperCamelCase__     )
             _A    		=  prev_t.item()

             self.assertEqual(UpperCamelCase__, UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Any     )  ->			Optional[int]:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  [1_00, 87, 50, 51, 0]

        with self.assertRaises(UpperCamelCase__, msg='`custom_timesteps` must be in descending order.'     ):
             scheduler.set_timesteps(timesteps=UpperCamelCase__     )
   def 	__UpperCAmelCase   (      self      :			Any     )  ->			Dict:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  [1_00, 87, 50, 1, 0]
        _A    		=  len(UpperCamelCase__     )

        with self.assertRaises(UpperCamelCase__, msg='Can only pass one of `num_inference_steps` or `custom_timesteps`.'     ):
             scheduler.set_timesteps(num_inference_steps=UpperCamelCase__, timesteps=UpperCamelCase__     )

   def 	__UpperCAmelCase   (      self      :			Dict     )  ->			Dict:
        _A    		=  self.scheduler_classes[0]
        _A    		=  self.get_scheduler_config()
        _A    		=  scheduler_class(**UpperCamelCase__     )

        _A    		=  [scheduler.config.num_train_timesteps]

        with self.assertRaises(
            UpperCamelCase__, msg='`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}', ):
             scheduler.set_timesteps(timesteps=UpperCamelCase__     )











'''simple docstring'''





_UpperCamelCase						:						Dict  =					range(2, 20 + 1)
_UpperCamelCase						:						str  =					[10**k for k in range(ks[-1] + 1)]
_UpperCamelCase						:						dict[int, dict[int, list[list[int]]]]  =					{}
def __UpperCAmelCase   (					A					:			List[Any]			,       A					:			str			,       A					:			Union[str, Any]			,       A					:			Union[str, Any]		)    ->   Optional[Any]:
			UpperCAmelCase_      :       Optional[Any]          =       sum(a_i[j] for j in range(A			,       len(A		)		)		)
			UpperCAmelCase_      :       Union[str, Any]          =       sum(a_i[j] * base[j] for j in range(min(len(A		)			,       A		)		)		)

			UpperCAmelCase_    ,      UpperCAmelCase_      :       Optional[int]          =       0, 0
			UpperCAmelCase_      :       str          =       n - i

			UpperCAmelCase_      :       Union[str, Any]          =       memo.get(A		)

			if sub_memo is not None:
						UpperCAmelCase_      :       Dict          =       sub_memo.get(A		)

						if jumps is not None and len(A		) > 0:
									# find and make the largest jump without going over
									UpperCAmelCase_      :       str          =       -1
									for _k in range(len(A		) - 1			,       -1			,       -1		):
												if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
															UpperCAmelCase_      :       Any          =       _k
															break

									if max_jump >= 0:
												UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_      :       Any          =       jumps[max_jump]
												# since the difference between jumps is cached, add c
												UpperCAmelCase_      :       Union[str, Any]          =       diff + c
												for j in range(min(A			,       len(A		)		)		):
															UpperCAmelCase_    ,      UpperCAmelCase_      :       Tuple          =       divmod(A			,       1_0		)
												if new_c > 0:
															add(A			,       A			,       A		)

						else:
									UpperCAmelCase_      :       Tuple          =       []
			else:
						UpperCAmelCase_      :       List[str]          =       {c: []}
						UpperCAmelCase_      :       List[str]          =       sub_memo

			if dn >= max_dn or c + diff >= base[k]:
						return diff, dn

			if k > ks[0]:
						while True:
									# keep doing smaller jumps
									UpperCAmelCase_    ,      UpperCAmelCase_      :       Optional[Any]          =       next_term(A			,       k - 1			,       i + dn			,       A		)
									diff += _diff
									dn += terms_jumped

									if dn >= max_dn or c + diff >= base[k]:
												break
			else:
						# would be too small a jump, just compute sequential terms instead
						UpperCAmelCase_    ,      UpperCAmelCase_      :       int          =       compute(A			,       A			,       i + dn			,       A		)
						diff += _diff
						dn += terms_jumped

			UpperCAmelCase_      :       List[str]          =       sub_memo[c]

			# keep jumps sorted by # of terms skipped
			UpperCAmelCase_      :       List[Any]          =       0
			while j < len(A		):
						if jumps[j][1] > dn:
									break
						j += 1

			# cache the jump for this value digitsum(b) and c
			sub_memo[c].insert(A			,       (diff, dn, k)		)
			return (diff, dn)
def __UpperCAmelCase   (					A					:			List[str]			,       A					:			Dict			,       A					:			List[str]			,       A					:			Union[str, Any]		)    ->   str:
			if i >= n:
						return 0, i
			if k > len(A		):
						a_i.extend([0 for _ in range(k - len(A		)		)]		)

			# note: a_i -> b * 10^k + c
			# ds_b -> digitsum(b)
			# ds_c -> digitsum(c)
			UpperCAmelCase_      :       int          =       i
			UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_      :       List[Any]          =       0, 0, 0
			for j in range(len(A		)		):
						if j >= k:
									ds_b += a_i[j]
						else:
									ds_c += a_i[j]

			while i < n:
						i += 1
						UpperCAmelCase_      :       Optional[int]          =       ds_c + ds_b
						diff += addend
						UpperCAmelCase_      :       Any          =       0
						for j in range(A		):
									UpperCAmelCase_      :       Dict          =       a_i[j] + addend
									UpperCAmelCase_    ,      UpperCAmelCase_      :       Tuple          =       divmod(A			,       1_0		)

									ds_c += a_i[j]

						if addend > 0:
									break

			if addend > 0:
						add(A			,       A			,       A		)
			return diff, i - start_i
def __UpperCAmelCase   (					A					:			Dict			,       A					:			Union[str, Any]			,       A					:			str		)    ->   List[Any]:
			for j in range(A			,       len(A		)		):
						UpperCAmelCase_      :       List[str]          =       digits[j] + addend
						if s >= 1_0:
									UpperCAmelCase_    ,      UpperCAmelCase_      :       Any          =       divmod(A			,       1_0		)
									UpperCAmelCase_      :       str          =       addend // 1_0 + quotient
						else:
									UpperCAmelCase_      :       Any          =       s
									UpperCAmelCase_      :       Any          =       addend // 1_0

						if addend == 0:
									break

			while addend > 0:
						UpperCAmelCase_    ,      UpperCAmelCase_      :       Union[str, Any]          =       divmod(A			,       1_0		)
						digits.append(A		)
def __UpperCAmelCase   (					A					:			int = 1_0**1_5		)    ->   int:
			UpperCAmelCase_      :       Any          =       [1]
			UpperCAmelCase_      :       Union[str, Any]          =       1
			UpperCAmelCase_      :       List[Any]          =       0
			while True:
						UpperCAmelCase_    ,      UpperCAmelCase_      :       str          =       next_term(A			,       2_0			,       i + dn			,       A		)
						dn += terms_jumped
						if dn == n - i:
									break

			UpperCAmelCase_      :       Any          =       0
			for j in range(len(A		)		):
						a_n += digits[j] * 1_0**j
			return a_n


if __name__ == "__main__":
						print(f'''{solution() = }''')


